1. Field of the Invention
The present invention relates to a differential amplifier and, particularly, to a differential amplifier that includes a differential pair in an input section.
2. Description of Related Art
A differential amplifier is widely used in an electronic circuit in order to perform signal amplification and signal processing operation. An example of a differential amplifier is disclosed in Behzad Razavi, “Design of Analog CMOS Integrated Circuit”, McGraw-Hill Higher Education, 2002, pp 325 (Behzad). FIG. 5 shows a circuit diagram of a differential amplifier 100 disclosed in Behzad.
Referring to FIG. 5, the differential amplifier 100 includes transistors M101 to M109, M10A and M10B, voltage sources V101 to V104, input terminals IP and IM, an output terminal OUT, a power supply terminal VDD and a ground terminal GND. The transistors M101 to M107 are NMOS transistors, and the transistors M108, M109, M10A and M10B are PMOS transistors.
In the differential amplifier 100, an operating current, which is generated by the transistor M101 based on a voltage of the voltage source V101, is supplied to a differential pair formed by the transistors M102 and M103. Based on the operating current, the differential pair generates a differential-mode current according to input signals that are input through the input terminals IP and IM. The differential-mode current involves currents I102 and I103. Further, in the differential amplifier 100, reference currents I10A and I10B are generated. The reference current I10A is generated by the transistor M10A based on a voltage of the voltage source V102, and the reference current I10B is generated by the transistor M10B based on a voltage of the voltage source V102. The reference currents I10A and I10B have the same current value.
A result of subtracting the current I102 from the reference current I10A is a current I108. The current I108 becomes a current I105 after flowing through a current mirror circuit that is formed by the transistors M104 and M105. The current I105 serves as an output sink current to the output terminal OUT. On the other hand, a result of subtracting the current I103 from the reference current I10B is a current I109. The current I109 serves as an output source current to the output terminal OUT. In this manner, in the differential amplifier 100, the output source current and the output sink current to the output terminal OUT are generated based on the input signals.
The transistors M108 and M109 control the drains of the transistors M10A and M10B so as to maintain a constant voltage based on a voltage of the voltage source V103. The transistors M106 and M107 control the drains of the transistors M104 and M105 so as to maintain a constant voltage based on a voltage of the voltage source V104.
The currents I102, I103, I105, I109 and a voltage gain av are described hereinafter. The current I102 can be represented by the following expression (1) when a mutual conductance of the transistor M102 is gm102 and an input signal through the input terminal IP is VIP. The current I103 can be represented by the following expression (2) when a mutual conductance of the transistor M103 is gm103 and an input signal through the input terminal IM is VIM. The mutual conductance gm102 and gm103 are the same value.
                              I          ⁢                                          ⁢          102                =                              gm            ⁢                                                  ⁢            102            *            VIP                    +                                    I              ⁢                                                          ⁢              101                        2                                              (        1        )                                          I          ⁢                                          ⁢          103                =                                            gm              ⁢                                                          ⁢              103              *              VIM                        +                          I101              2                                =                                    gm              ⁢                                                          ⁢              102              *              VIM                        +                                          I                ⁢                                                                  ⁢                101                            2                                                          (        2        )            
The reference currents I10A and I10B can be represented by the following expressions (3) and (4), respectively.I10A=I102+I108=I102+I105  (3)I10B=I103+I109  (4)
Based on the expressions (1) and (3), the output sink current I105 can be represented by the following expression (5). Based on the expressions (2) and (4), the output source current I109 can be represented by the following expression (6).
                                                                        I                ⁢                                                                  ⁢                105                            =                                                I                  ⁢                                                                          ⁢                  10                  ⁢                                                                          ⁢                  A                                -                                  I                  ⁢                                                                          ⁢                  02                                                                                                        =                                                I                  ⁢                                                                          ⁢                  10                  ⁢                                                                          ⁢                  A                                -                                  (                                                            gm                      ⁢                                                                                          ⁢                      102                      *                      VIP                                        +                                                                  I                        ⁢                                                                                                  ⁢                        101                                            2                                                        )                                                                                        (        5        )                                                                                    I                ⁢                                                                  ⁢                109                            =                                                I                  ⁢                                                                          ⁢                  10                  ⁢                                                                          ⁢                  B                                -                                  I                  ⁢                                                                          ⁢                  03                                                                                                        =                                                I                  ⁢                                                                          ⁢                  10                  ⁢                                                                          ⁢                  B                                -                                  (                                                            gm                      ⁢                                                                                          ⁢                      102                      *                      VIM                                        +                                                                  I                        ⁢                                                                                                  ⁢                        101                                            2                                                        )                                                                                        (        6        )            
A differential-mode component vo of an output voltage of the differential amplifier 100 can be represented by the following expression (7) when a drain resistance of the transistor M109 connected to the output terminal OUT is Rds109 and a drain resistance of the transistor M107 connected to the output terminal OUT is Rds107. In the expression (7), vip indicates the signal level of a differential-mode component of the input signal VIP, and vim indicates the signal level of a differential-mode component of the input signal VIM.
                                                        vo              =                            ⁢                                                (                                                            Rds                      ⁢                                                                                          ⁢                      109                                        //                                          Rds                      ⁢                                                                                          ⁢                      107                                                        )                                *                                  (                                                            I                      ⁢                                                                                          ⁢                      109                                        -                                          I                      ⁢                                                                                          ⁢                      105                                                        )                                                                                                        =                            ⁢                                                (                                                            Rds                      ⁢                                                                                          ⁢                      109                                        //                                          Rds                      ⁢                                                                                          ⁢                      107                                                        )                                *                                  (                                                                                                                                          I                            ⁢                                                                                                                  ⁢                            10                            ⁢                                                                                                                  ⁢                            B                                                    -                                                      (                                                                                          gm                                ⁢                                                                                                                                  ⁢                                102                                *                                VIM                                                            +                                                                                                I                                  ⁢                                                                                                                                          ⁢                                  101                                                                2                                                                                      )                                                    -                                                                                                                                                                                          I                            ⁢                                                                                                                  ⁢                            10                            ⁢                                                                                                                  ⁢                            A                                                    +                                                      (                                                                                          gm                                ⁢                                                                                                                                  ⁢                                102                                *                                VIP                                                            +                                                                                                I                                  ⁢                                                                                                                                          ⁢                                  101                                                                2                                                                                      )                                                                                                                                )                                                                                                        =                            ⁢                                                (                                                            Rds                      ⁢                                                                                          ⁢                      109                                        //                                          Rds                      ⁢                                                                                          ⁢                      107                                                        )                                *                gm                ⁢                                                                  ⁢                102                *                                  (                                                            -                      vim                                        +                    vip                                    )                                                                                        (        7        )            
The voltage gain av of the differential amplifier 100 is represented by the following expression (8) from the output voltage represented by the expression (7).
                    av        =                              vo                          (                                                -                  vim                                +                vip                            )                                =                      gm            ⁢                                                  ⁢            102            *                          (                                                Rds                  ⁢                                                                          ⁢                  109                                //                                  Rds                  ⁢                                                                          ⁢                  107                                            )                                                          (        8        )            